The tdistribution¶
The tdistribution arises in statistics. If \(Y_1\) has a normal distribution and \(Y_2\) has a chisquared distribution with \(\nu\) degrees of freedom then the ratio,
\[X = { Y_1 \over \sqrt{Y_2 / \nu} }\]
has a tdistribution \(t(x;\nu)\) with \(\nu\) degrees of freedom.

gsl_ran_tdist
(nu)¶ This function returns a random variate from the tdistribution. The distribution function is,
\[p(x) dx = {\Gamma((\nu + 1)/2) \over \sqrt{\pi \nu} \Gamma(\nu/2)} (1 + x^2/\nu)^{(\nu + 1)/2} dx\]for \(\infty < x < +\infty\).

gsl_ran_tdist_pdf
(x, nu)¶ This function computes the probability density \(p(x)\) at \(x\) for a tdistribution with
nu
degrees of freedom, using the formula given above.

gsl_cdf_tdist_P
(x, nu)¶

gsl_cdf_tdist_Q
(x, nu)¶

gsl_cdf_tdist_Pinv
(P, nu)¶

gsl_cdf_tdist_Qinv
(Q, nu)¶ These functions compute the cumulative distribution functions \(P(x), Q(x)\) and their inverses for the tdistribution with
nu
degrees of freedom.